Question: Little Johnny is walking home. He has $300 he has to bring home to his mom. While he is walking a man stops him and gives him a chance to double his money. The man says "I'll give you $600 if you can roll 1 die and get a 4 or above, you can roll 2 dice and get a 5 or 6 on at least one of them, or you can roll 3 dice and get a 6 on at least on die. If you don't I get your $300."
What does Johnny do to have the best chance of getting home with the money?
Answer: He just doesn't take the bet. This gives him a 100 percent chance of getting the money home. If he takes the bet with 1 die he has a 50 percent chance of winning. If he takes the bet with 2 dice he has about a 56 percent chance of winning. If he takes the bet with 3 dice he has about a 42 percent chance of winning.
Question: A hobo picks up cigarette butts from the ground and can make a cigarette with 4 butts. If he finds 16 cigarette butts, how many cigarettes can he make?
Answer: 5. He makes 4 cigarettes with the 16 butts. Then he smokes them and has 4 more butts to make another cigarette.
Question: Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a sports car; behind all of the others is bicycles. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 2, revealing a bicycle. He then says to you, "Do you want to pick door No. 3?" Is it to your advantage to switch your choice?
Answer: Yes, by changing your answer your chances of winning actually goes up from 1/3 to 2/3.
This becomes obvious when expanding the example. Suppose there was 100 doors rather than 3. You pick one and the host shows you that the car is not behind 98 of the doors then asks you to switch to the remaining door or keep the door you picked. Of course you would switch your door because chances are you didn't pick the correct door initially.
For more explanation go to http://en.wikipedia.org/wiki/Monty_Hall_problem#Solutions
Question: A claustrophobic person gets on a train. The train enters a tunnel just as it is leaving the station.
Where is the best place for him to sit?
Answer: In the back. The train will be accelerating so it will be going faster when the back of the train enters the tunnel so a person in the back will spend less time in the tunnel.
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